What is the value of p?
A frequency distribution table is given below:<br><br> <table> <thead><tr><th>X</th><th>0</th><th>1</th><th>2</th><th>3</th><th>4</th><th>5</th></tr></thead> <tbody> <tr><td>f</td><td>46</td><td>p</td><td>q</td><td>25</td><td>10</td><td>5</td></tr> </tbody> </table><br><br> Total frequency is 200 and mean of the distribution is 1.46.
- A. 70
- B. 72
- C. 76 ✓
- D. 78
Correct Answer: C. 76
Explanation
Total frequency \sum f = 46 + p + q + 25 + 10 + 5 = 200 \implies p + q = 114. The mean formula yields \sum (f \cdot x) = 0 + p + 2q + 75 + 40 + 25 = 200 \times 1.46 = 292 \implies p + 2q = 152. Solving the system gives q = 38 and p = 76.
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